You are building a design matrix for a linear model. The categorical feature city has three levels (A, B, C) and has been one-hot encoded into three columns. Alongside it sit a scaled numeric feature age and the usual bias column of all ones. Six training rows:
| bias | city_A | city_B | city_C | age |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 2 |
| 1 | 1 | 0 | 0 | 4 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 3 |
| 1 | 0 | 0 | 1 | 5 |
| 1 | 0 | 0 | 1 | 0 |
Read each of the columns as a vector in . What is the dimension of the subspace of that these five columns span (the column space of the design matrix)?
Once you get it right, the reasoning behind the answer shows up here.
Select all that apply.